A design methodology is presented for synthesizing a high-performance articulating robot manipulator fabricated with optimally tailored composite laminates. By optimally specifying the geometric configurations, the types of fiber, matrix, stacking sequence, fiber volume fraction, fiber layups, etc., the synthesized composite material may possess such superior characteristics as high damping, high stiffness, high strength and low mass. In accordance with the design requirements, e.g. minimum deflection during articulating motion or fast settling time after the power has been stopped, the design objectives and constraint conditions were specified. As an illustrative example, a two-link robot manipulator fabricated with the aforementioned composite laminates is employed for demonstrating the proposed design methodology.